Dynamic Local Search for the Maximum Clique Problem

TL;DR

This paper presents DLS-MC, a stochastic local search algorithm for the maximum clique problem that dynamically adjusts vertex penalties and employs perturbation to improve search efficiency and outperform existing algorithms.

Contribution

Introduction of DLS-MC, a novel local search algorithm that uses dynamic penalty adjustments and perturbation to effectively solve the maximum clique problem.

Findings

DLS-MC outperforms state-of-the-art algorithms on DIMACS benchmarks.

The penalty delay parameter effectively controls search behavior.

DLS-MC demonstrates substantial performance improvements across various instances.

Abstract

In this paper, we introduce DLS-MC, a new stochastic local search algorithm for the maximum clique problem. DLS-MC alternates between phases of iterative improvement, during which suitable vertices are added to the current clique, and plateau search, during which vertices of the current clique are swapped with vertices not contained in the current clique. The selection of vertices is solely based on vertex penalties that are dynamically adjusted during the search, and a perturbation mechanism is used to overcome search stagnation. The behaviour of DLS-MC is controlled by a single parameter, penalty delay, which controls the frequency at which vertex penalties are reduced. We show empirically that DLS-MC achieves substantial performance improvements over state-of-the-art algorithms for the maximum clique problem over a large range of the commonly used DIMACS benchmark instances.